The validity of the chain of custody boils down to the cops and government in general being trusted enough to not falsify it when it suits them.

There are ways to cryptographically validate chain of custody. If we're in a world where only video with valid chain of custody can be used in court then those methods will see widespread adoption. You also didn't address any of the other kinds of evidence that I mentioned AI being unable to tamper with. Sure, you can generate a video of someone doing something horrible. But in a world where it is known that you can generate such videos, what jury would ever convict someone based solely on a video like that? It's frankly ridiculous.

This is very much the typical fictional dystopia scenario where one assumes all the possible negative uses of the technology will work fine but ignore all the ways of being able to counter those negative uses. You can spin a scary sci-fi tale from such speculation but it's not really a useful way of predicting how the actual future is likely to go.